The existence and nonexistence for time nonlocal evolution equations with superlinear sources

Xi Huang; Li Peng

The existence and nonexistence for time nonlocal evolution equations with superlinear sources

Analysis of PDEs 2026-07-14 v1

Authors: Xi Huang , Li Peng

Abstract

We consider the solvable behaviour for the initial value problem of time nonlocal evolution equations with the kernels of type $(\mathcal{PC})$ . Our aim is to analyze some sufficient conditions ensuring local existence, integrability of mild solutions when the nonlinear term exhibits rapid growth. Moreover, a sufficient condition of the unsolvable result is also established. It turns out that the solvable behaviour is closely connected with the index on the initial value, which occurs a critical dimension phenomenon. The proofs rely on subordination and monotone iterative method. Finally, several examples are given to illustrate the wide applicability of the results.

Cite

@article{arxiv.2607.13177,
  title  = {The existence and nonexistence for time nonlocal evolution equations with superlinear sources},
  author = {Xi Huang and Li Peng},
  journal= {arXiv preprint arXiv:2607.13177},
  year   = {2026}
}